Learning Graph Representations in Normed Spaces

Diaaeldin Taha, Wei Zhao, J. Maxwell Riestenberg, Michael Strube

Keywords: normed spaces, graph embeddings, geometric deep learning, metric learning, riemannian manifold learning

TL;DR: We propose using normed spaces other than L2 for graph embeddings, particularly as a complement to several popular Riemannian manifolds.

Abstract:

Theoretical results from discrete geometry suggest that normed spaces can abstractly embed finite metric spaces with surprisingly low theoretical bounds on distortion in low dimensions.
In this paper, inspired by this theoretical insight, we propose normed spaces as a more flexible and computationally efficient alternative to several popular Riemannian manifolds for learning graph embeddings.
Our normed space embeddings significantly outperform several popular manifolds on a large range of synthetic and real-world graph reconstruction benchmark datasets while requiring significantly fewer computational resources.
We also empirically verify the superiority of normed space embeddings on growing families of graphs associated with negative, zero, and positive curvature, further reinforcing the flexibility of normed spaces in capturing diverse graph structures as graph sizes increase.
Lastly, we demonstrate the utility of normed space embeddings on two applied graph embedding tasks, namely, link prediction and recommender systems.
Our work highlights the potential of normed spaces for geometric graph representation learning, raises new research questions, and offers a valuable tool for experimental mathematics in the field of finite metric space embeddings.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 2126